I trained many moons ago as a pharmacist and pharmacologist, and medicinal leeches were (and still are) widely used in research, and are making a comeback in some fields of medicine.
We used to use the European medicinal leech (Hirudo medicinalis), and I can assure you that most examples are far from small (anything up to 9 inches long and an inch in diameter when satiated on blood).
We kept our leeches in a little water in plain cylindrical stoppered glass jars (anything up to a 100 leeches in a 5 litre jar) and they were fed on chunks of liver and clotted blood. They were notoriously good escapologists, quite capable of pushing the stoppers out of the jars, and we used to tie muslin tightly round the tops of the jars to try and keep them contained. It was not unusual to come into the laboratory in a morning to find large, juicy, escaped leeches attached to just about any surface.
Satiated leeches are not too gross to deal with, but hungry leeches can, and do, bite quite readily, and are fairly difficult to remove from skin without harming them until they have finished their meal.
Fred.